Unexpected doping effects on phonon transport in quasi-one-dimensional van der Waals crystal TiS3 nanoribbons

Doping usually reduces lattice thermal conductivity because of enhanced phonon-impurity scattering. Here, we report unexpected doping effects on the lattice thermal conductivity of quasi-one-dimensional (quasi-1D) van der Waals (vdW) TiS3 nanoribbons. As the nanoribbon thickness reduces from ~80 to ~19 nm, the concentration of oxygen atoms has a monotonic increase along with a 7.4-fold enhancement in the thermal conductivity at room temperature. Through material characterizations and atomistic modellings, we find oxygen atoms diffuse more readily into thinner nanoribbons and more sulfur atoms are substituted. The doped oxygen atoms induce significant lattice contraction and coupling strength enhancement along the molecular chain direction while have little effect on vdW interactions, different from that doping atoms induce potential and structural distortions along all three-dimensional directions in 3D materials. With the enhancement of coupling strength, Young’s modulus is enhanced while phonon-impurity scattering strength is suppressed, significantly improving the phonon thermal transport.


2 . 3 .Supplementary Figure 4 .Supplementary Figure 5 .Supplementary Figure 9 . 10 . 9 .Supplementary Figure 11 .
. Thermal measurements of TiS3 nanoribbons.(a) Comparison of the temperature T dependent thermal conductance G from three individual measurements.The SEM images of a 62 nm thick and 231 nm wide nanoribbon contacting with the electrodes with two (b) and four contact regions (c) that are deposited with a thin Pt film by electron beam induced-deposition (EBID), respectively.Measured thermal conductivities κ of TiS3 nanoribbons along the b-axis direction versus temperature T with different widths.Electrical conductivity σ of TiS3 nanoribbons as a function of temperature T. Measurements of Young's modulus.(a) Scheme of Young's modulus measurement via three-point bending methods.(b) An AFM topography displaying a TiS3 nanoribbon suspended on a Si trench.Force-deflection curves of 34 nm (c) and 154 nm (d) thick samples, respectively.The black, pink and blue curves represent the extension, retraction and fitting results, respectively.Measurements of length dependent thermal conductivity κ. (a-d) SEM micrographs of TiS3 nanoribbon (with weight W of 98 nm and thickness H of 26 nm) at different suspended lengths L between the heating and sensing membranes.(e) Temperature T dependent thermal conductivity.(f) Length L dependent thermal conductivity at room temperature.Structural relaxation for TiS3 with one S defect-1 (a), one S defect-2 (b), two S defects (c) and two O substitution (d).The yellow, blue and red balls in (a)-(d) represent S, Ti and O atoms, respectively.Phonon dispersions of TiS3 with one S defect-1 (a), one S defect-2 (b), two S defects (c) and two O substitution (d) as shown in Supplementary Figure Calculated thermal conductivities κ of pristine TiS3, TiS3 with two S defects and TiS3 with two O substitution as shown in Supplementary Figure

Supplementary Figure 12 .
Atomic structure of TiS3 with O atoms substitution (a) and without O atoms substitution (b).The blue, yellow and red atoms represent Ti, S and O atoms, respectively.The S-O bond length is 0.1703 nm and S-S bond length is 0.2041 nm.Supplementary Figure 13.Phonon dispersions of TiS3 (a) and TiS2O1 (b).Supplementary Figure 14.Phonon properties of pristine TiS3 and O doped TiS3.(a) Temperature-dependent specific heat of TiS3 with different O concentrations.(b) Phonon lifetime as a function of phonon frequency in different O concentrations at 300 K.

15 . 17 . 19 .
Lattice contraction rates (a) and O atomic fraction (b) as a function of width in TiS3 nanoribbons with similar thickness.The error bars of lattice contraction rates in (a) are from the variations among several individual measurements (see Supplementary Note 6).The error bars in (b) indicate the deviations from integration of O peak obtained from EDS mapping Supplementary Figure 16.Phonon-phonon scattering rates of TiS3, TiS2O and TiS2F as a function of phonon frequency at 300 K. Temperature-dependent thermal conductivity κ of TiS3 (red circles) and F atoms doped TiS3 (olive diamonds).The dots and lines represent firstprinciples calculations and Callaway fitting results, respectively.Supplementary Figure 18.Core-shell model to estimate the thermal conductivity of TiS3 nanoribbons.(a) The core-shell structure of TiS3.t1, t2, W and L are the thickness of shell and core, and the width and length of core-shell structure, respectively.(b) The shell thickness t1 dependent effective thermal conductivity keff of the core-shell structure for the 19 nm sample.Evolution of the O atom distribution across the bc plane of a TiS3 nanoribbon with the elapse of time.

Table 2 .
Lattice constants, total energy per unit cell and lattice contraction rates of different structures as shown in Supplementary Fig.9.

Table 3 .
Thermal conductivity of TiO2 at room temperature from experimental measurement and first-principles calculation.

Table 4 .
Thickness dependent thermal conductivity with and without lattice contraction enhanced group velocity at room temperature from Callaway model fitting.

Table 5 .
Thickness dependent thermal conductivity with and without phonon-boundary scattering at room temperature from Callaway model fitting.